Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
224 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23782754 | C3 | semidirect |
| 4. #23782753 | C3 | semidirect |
| 5. #23782752 | C3 | semidirect |
| 6. C43×#6880 | C3 | semidirect |
| 50. #6880 | C43⋊C3 | direct (N × H) |
| 55. C43⋊C3 | #6880 | direct (N × H) |
| 66. C43 | C3×#6880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C43⋊C3 | 3 |
| C92×C43⋊C3 | 3 |
| #23782754 | 3 |
| #23782753 | 3 |
| #23782752 | 3 |
| C43×#6880 | 3 |
| C3×#6880 | 43 |